20.02/6.94 YES 20.02/6.95 proof of /export/starexec/sandbox/benchmark/theBenchmark.c 20.02/6.95 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 20.02/6.95 20.02/6.95 20.02/6.95 Termination of the given C Problem could be proven: 20.02/6.95 20.02/6.95 (0) C Problem 20.02/6.95 (1) CToLLVMProof [EQUIVALENT, 171 ms] 20.02/6.95 (2) LLVM problem 20.02/6.95 (3) LLVMToTerminationGraphProof [EQUIVALENT, 2695 ms] 20.02/6.95 (4) LLVM Symbolic Execution Graph 20.02/6.95 (5) SymbolicExecutionGraphToSCCProof [SOUND, 0 ms] 20.02/6.95 (6) AND 20.02/6.95 (7) LLVM Symbolic Execution SCC 20.02/6.95 (8) SCC2IRS [SOUND, 52 ms] 20.02/6.95 (9) IntTRS 20.02/6.95 (10) IntTRSCompressionProof [EQUIVALENT, 0 ms] 20.02/6.95 (11) IntTRS 20.02/6.95 (12) RankingReductionPairProof [EQUIVALENT, 24 ms] 20.02/6.95 (13) YES 20.02/6.95 (14) LLVM Symbolic Execution SCC 20.02/6.95 (15) SCC2IRS [SOUND, 75 ms] 20.02/6.95 (16) IntTRS 20.02/6.95 (17) IntTRSCompressionProof [EQUIVALENT, 0 ms] 20.02/6.95 (18) IntTRS 20.02/6.95 (19) RankingReductionPairProof [EQUIVALENT, 10 ms] 20.02/6.95 (20) YES 20.02/6.95 20.02/6.95 20.02/6.95 ---------------------------------------- 20.02/6.95 20.02/6.95 (0) 20.02/6.95 Obligation: 20.02/6.95 c file /export/starexec/sandbox/benchmark/theBenchmark.c 20.02/6.95 ---------------------------------------- 20.02/6.95 20.02/6.95 (1) CToLLVMProof (EQUIVALENT) 20.02/6.95 Compiled c-file /export/starexec/sandbox/benchmark/theBenchmark.c to LLVM. 20.02/6.95 ---------------------------------------- 20.02/6.95 20.02/6.95 (2) 20.02/6.95 Obligation: 20.02/6.95 LLVM Problem 20.02/6.95 20.02/6.95 Aliases: 20.02/6.95 20.02/6.95 Data layout: 20.02/6.95 20.02/6.95 "e-p:64:64:64-i1:8:8-i8:8:8-i16:16:16-i32:32:32-i64:64:64-f32:32:32-f64:64:64-v64:64:64-v128:128:128-a0:0:64-s0:64:64-f80:128:128-n8:16:32:64-S128" 20.02/6.95 20.02/6.95 Machine: 20.02/6.95 20.02/6.95 "x86_64-pc-linux-gnu" 20.02/6.95 20.02/6.95 Type definitions: 20.02/6.95 20.02/6.95 Global variables: 20.02/6.95 20.02/6.95 Function declarations and definitions: 20.02/6.95 20.02/6.95 *BasicFunctionTypename: "main" linkageType: EXTERNALLY_VISIBLE returnParam: i32 parameters: () variableLength: false visibilityType: DEFAULT callingConvention: ccc 20.02/6.95 0: 20.02/6.95 %1 = alloca i32, align 4 20.02/6.95 %i = alloca *i32, align 8 20.02/6.95 %j = alloca *i32, align 8 20.02/6.95 %c = alloca *i32, align 8 20.02/6.95 store 0, %1 20.02/6.95 %2 = alloca i8, numElementsLit: 4 20.02/6.95 %3 = bitcast *i8 %2 to *i32 20.02/6.95 store %3, %i 20.02/6.95 %4 = alloca i8, numElementsLit: 4 20.02/6.95 %5 = bitcast *i8 %4 to *i32 20.02/6.95 store %5, %j 20.02/6.95 %6 = alloca i8, numElementsLit: 4 20.02/6.95 %7 = bitcast *i8 %6 to *i32 20.02/6.96 store %7, %c 20.02/6.96 %8 = load %c 20.02/6.96 store 0, %8 20.02/6.96 %9 = load %i 20.02/6.96 store 0, %9 20.02/6.96 br %10 20.02/6.96 10: 20.02/6.96 %11 = load %i 20.02/6.96 %12 = load %11 20.02/6.96 %13 = icmp slt %12 100 20.02/6.96 br %13, %14, %23 20.02/6.96 14: 20.02/6.96 %15 = load %c 20.02/6.96 %16 = load %15 20.02/6.96 %17 = add %16 1 20.02/6.96 %18 = load %c 20.02/6.96 store %17, %18 20.02/6.96 br %19 20.02/6.96 19: 20.02/6.96 %20 = load %i 20.02/6.96 %21 = load %20 20.02/6.96 %22 = add %21 1 20.02/6.96 store %22, %20 20.02/6.96 br %10 20.02/6.96 23: 20.02/6.96 %24 = load %j 20.02/6.96 store 5, %24 20.02/6.96 br %25 20.02/6.96 25: 20.02/6.96 %26 = load %j 20.02/6.96 %27 = load %26 20.02/6.96 %28 = icmp slt %27 21 20.02/6.96 br %28, %29, %38 20.02/6.96 29: 20.02/6.96 %30 = load %c 20.02/6.96 %31 = load %30 20.02/6.96 %32 = add %31 1 20.02/6.96 %33 = load %c 20.02/6.96 store %32, %33 20.02/6.96 br %34 20.02/6.96 34: 20.02/6.96 %35 = load %j 20.02/6.96 %36 = load %35 20.02/6.96 %37 = add %36 3 20.02/6.96 store %37, %35 20.02/6.96 br %25 20.02/6.96 38: 20.02/6.96 %39 = load %c 20.02/6.96 %40 = load %39 20.02/6.96 ret %40 20.02/6.96 20.02/6.96 20.02/6.96 Analyze Termination of all function calls matching the pattern: 20.02/6.96 main() 20.02/6.96 ---------------------------------------- 20.02/6.96 20.02/6.96 (3) LLVMToTerminationGraphProof (EQUIVALENT) 20.02/6.96 Constructed symbolic execution graph for LLVM program and proved memory safety. 20.02/6.96 ---------------------------------------- 20.02/6.96 20.02/6.96 (4) 20.02/6.96 Obligation: 20.02/6.96 SE Graph 20.02/6.96 ---------------------------------------- 20.02/6.96 20.02/6.96 (5) SymbolicExecutionGraphToSCCProof (SOUND) 20.02/6.96 Splitted symbolic execution graph to 2 SCCs. 20.02/6.96 ---------------------------------------- 20.02/6.96 20.02/6.96 (6) 20.02/6.96 Complex Obligation (AND) 20.02/6.96 20.02/6.96 ---------------------------------------- 20.02/6.96 20.02/6.96 (7) 20.02/6.96 Obligation: 20.02/6.96 SCC 20.02/6.96 ---------------------------------------- 20.02/6.96 20.02/6.96 (8) SCC2IRS (SOUND) 20.02/6.96 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 20.02/6.96 Generated rules. Obtained 17 rulesP rules: 20.02/6.96 f_425(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v296, 1, v298, v299, v300, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 20, 101, 8, 23, 4) -> f_426(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v298, v299, v296, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 20, 101, 8, 23, 4) :|: 0 = 0 20.02/6.96 f_426(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v298, v299, v296, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 20, 101, 8, 23, 4) -> f_427(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v298, v299, v296, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 17, 101, 8, 20, 4) :|: v300 < 21 && v296 <= 17 20.02/6.96 f_427(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v298, v299, v296, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 17, 101, 8, 20, 4) -> f_429(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v298, v299, v296, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 17, 101, 8, 20, 4) :|: 0 = 0 20.02/6.96 f_429(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v298, v299, v296, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 17, 101, 8, 20, 4) -> f_431(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v298, v299, v296, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 17, 101, 8, 20, 4) :|: TRUE 20.02/6.96 f_431(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v298, v299, v296, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 17, 101, 8, 20, 4) -> f_433(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v298, v299, v296, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 17, 101, 8, 20, 4) :|: 0 = 0 20.02/6.96 f_433(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v298, v299, v296, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 17, 101, 8, 20, 4) -> f_435(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v299, v296, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 17, 101, 8, 20, 4) :|: 0 = 0 20.02/6.96 f_435(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v299, v296, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 17, 101, 8, 20, 4) -> f_437(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v299, v318, v296, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 17, 101, 8, 20, 4, 102) :|: v318 = 1 + v299 && 102 <= v318 20.02/6.96 f_437(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v299, v318, v296, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 17, 101, 8, 20, 4, 102) -> f_438(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v299, v318, v296, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 17, 101, 8, 20, 4, 102) :|: 0 = 0 20.02/6.96 f_438(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v299, v318, v296, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 17, 101, 8, 20, 4, 102) -> f_439(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v299, v318, v296, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 17, 101, 8, 20, 4, 102) :|: TRUE 20.02/6.96 f_439(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v299, v318, v296, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 17, 101, 8, 20, 4, 102) -> f_440(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v299, v318, v296, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 17, 101, 8, 20, 4, 102) :|: TRUE 20.02/6.96 f_440(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v299, v318, v296, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 17, 101, 8, 20, 4, 102) -> f_441(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v299, v318, v296, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 17, 101, 8, 20, 4, 102) :|: 0 = 0 20.02/6.96 f_441(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v299, v318, v296, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 17, 101, 8, 20, 4, 102) -> f_442(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v299, v318, v301, v302, v303, v304, v305, v306, v307, 3, 7, 101, 8, 20, 4, 102) :|: 0 = 0 20.02/6.96 f_442(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v299, v318, v301, v302, v303, v304, v305, v306, v307, 3, 7, 101, 8, 20, 4, 102) -> f_443(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v299, v318, v320, v301, v302, v303, v304, v305, v306, v307, 3, 7, 101, 8, 20, 4, 102, 11, 23) :|: v320 = 3 + v300 && 11 <= v320 && v320 <= 23 20.02/6.96 f_443(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v299, v318, v320, v301, v302, v303, v304, v305, v306, v307, 3, 7, 101, 8, 20, 4, 102, 11, 23) -> f_444(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v299, v318, v320, v301, v302, v303, v304, v305, v306, v307, 3, 7, 101, 8, 20, 4, 102, 11, 23) :|: TRUE 20.02/6.96 f_444(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v299, v318, v320, v301, v302, v303, v304, v305, v306, v307, 3, 7, 101, 8, 20, 4, 102, 11, 23) -> f_445(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v299, v318, v320, v301, v302, v303, v304, v305, v306, v307, 3, 7, 101, 8, 20, 4, 102, 11, 23) :|: TRUE 20.02/6.96 f_445(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v299, v318, v320, v301, v302, v303, v304, v305, v306, v307, 3, 7, 101, 8, 20, 4, 102, 11, 23) -> f_424(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v300, 1, v299, v318, v320, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 20, 101, 8, 23, 4) :|: TRUE 20.02/6.96 f_424(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v296, 1, v298, v299, v300, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 20, 101, 8, 23, 4) -> f_425(v286, v287, v288, v289, v290, v291, v292, 100, 0, 99, v296, 1, v298, v299, v300, v301, v302, v303, v304, v305, v306, v307, 3, 7, 5, 20, 101, 8, 23, 4) :|: 0 = 0 20.02/6.96 Combined rules. Obtained 1 rulesP rules: 20.02/6.96 f_425(v286:0, v287:0, v288:0, v289:0, v290:0, v291:0, v292:0, 100, 0, 99, v296:0, 1, v298:0, v299:0, v300:0, v301:0, v302:0, v303:0, v304:0, v305:0, v306:0, v307:0, 3, 7, 5, 20, 101, 8, 23, 4) -> f_425(v286:0, v287:0, v288:0, v289:0, v290:0, v291:0, v292:0, 100, 0, 99, v300:0, 1, v299:0, 1 + v299:0, 3 + v300:0, v301:0, v302:0, v303:0, v304:0, v305:0, v306:0, v307:0, 3, 7, 5, 20, 101, 8, 23, 4) :|: v296:0 < 18 && v300:0 < 21 && v299:0 > 100 && v300:0 > 7 20.02/6.96 Filtered unneeded arguments: 20.02/6.96 f_425(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30) -> f_425(x11, x14, x15) 20.02/6.96 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 20.02/6.96 f_425(v296:0, v299:0, v300:0) -> f_425(v300:0, 1 + v299:0, 3 + v300:0) :|: v300:0 < 21 && v296:0 < 18 && v300:0 > 7 && v299:0 > 100 20.02/6.96 20.02/6.96 ---------------------------------------- 20.02/6.96 20.02/6.96 (9) 20.02/6.96 Obligation: 20.02/6.96 Rules: 20.02/6.96 f_425(v296:0, v299:0, v300:0) -> f_425(v300:0, 1 + v299:0, 3 + v300:0) :|: v300:0 < 21 && v296:0 < 18 && v300:0 > 7 && v299:0 > 100 20.02/6.96 20.02/6.96 ---------------------------------------- 20.02/6.96 20.02/6.96 (10) IntTRSCompressionProof (EQUIVALENT) 20.02/6.96 Compressed rules. 20.02/6.96 ---------------------------------------- 20.02/6.96 20.02/6.96 (11) 20.02/6.96 Obligation: 20.02/6.96 Rules: 20.02/6.96 f_425(v296:0:0, v299:0:0, v300:0:0) -> f_425(v300:0:0, 1 + v299:0:0, 3 + v300:0:0) :|: v300:0:0 > 7 && v299:0:0 > 100 && v296:0:0 < 18 && v300:0:0 < 21 20.02/6.96 20.02/6.96 ---------------------------------------- 20.02/6.96 20.02/6.96 (12) RankingReductionPairProof (EQUIVALENT) 20.02/6.96 Interpretation: 20.02/6.96 [ f_425 ] = -1/3*f_425_3 20.02/6.96 20.02/6.96 The following rules are decreasing: 20.02/6.96 f_425(v296:0:0, v299:0:0, v300:0:0) -> f_425(v300:0:0, 1 + v299:0:0, 3 + v300:0:0) :|: v300:0:0 > 7 && v299:0:0 > 100 && v296:0:0 < 18 && v300:0:0 < 21 20.02/6.96 20.02/6.96 The following rules are bounded: 20.02/6.96 f_425(v296:0:0, v299:0:0, v300:0:0) -> f_425(v300:0:0, 1 + v299:0:0, 3 + v300:0:0) :|: v300:0:0 > 7 && v299:0:0 > 100 && v296:0:0 < 18 && v300:0:0 < 21 20.02/6.96 20.02/6.96 20.02/6.96 ---------------------------------------- 20.02/6.96 20.02/6.96 (13) 20.02/6.96 YES 20.02/6.96 20.02/6.96 ---------------------------------------- 20.02/6.96 20.02/6.96 (14) 20.02/6.96 Obligation: 20.02/6.96 SCC 20.02/6.96 ---------------------------------------- 20.02/6.96 20.02/6.96 (15) SCC2IRS (SOUND) 20.02/6.96 Transformed LLVM symbolic execution graph SCC into a rewrite problem. Log: 20.02/6.96 Generated rules. Obtained 17 rulesP rules: 20.02/6.96 f_340(v123, v124, v125, v126, v127, v128, v129, v130, 1, v132, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 99, 100, 4, 8) -> f_341(v123, v124, v125, v126, v127, v128, v129, v132, 1, v130, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 99, 100, 4, 8) :|: 0 = 0 20.02/6.96 f_341(v123, v124, v125, v126, v127, v128, v129, v132, 1, v130, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 99, 100, 4, 8) -> f_342(v123, v124, v125, v126, v127, v128, v129, v132, 1, v130, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 98, 99, 4, 8) :|: v132 < 100 && v130 <= 98 20.02/6.96 f_342(v123, v124, v125, v126, v127, v128, v129, v132, 1, v130, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 98, 99, 4, 8) -> f_344(v123, v124, v125, v126, v127, v128, v129, v132, 1, v130, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 98, 99, 4, 8) :|: 0 = 0 20.02/6.96 f_344(v123, v124, v125, v126, v127, v128, v129, v132, 1, v130, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 98, 99, 4, 8) -> f_346(v123, v124, v125, v126, v127, v128, v129, v132, 1, v130, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 98, 99, 4, 8) :|: TRUE 20.02/6.96 f_346(v123, v124, v125, v126, v127, v128, v129, v132, 1, v130, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 98, 99, 4, 8) -> f_348(v123, v124, v125, v126, v127, v128, v129, v132, 1, v130, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 98, 99, 4, 8) :|: 0 = 0 20.02/6.96 f_348(v123, v124, v125, v126, v127, v128, v129, v132, 1, v130, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 98, 99, 4, 8) -> f_350(v123, v124, v125, v126, v127, v128, v129, v132, 1, v130, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 98, 99, 4, 8) :|: 0 = 0 20.02/6.96 f_350(v123, v124, v125, v126, v127, v128, v129, v132, 1, v130, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 98, 99, 4, 8) -> f_352(v123, v124, v125, v126, v127, v128, v129, v132, 1, v141, v130, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 98, 99, 4, 8, 2, 100) :|: v141 = 1 + v132 && 2 <= v141 && v141 <= 100 20.02/6.96 f_352(v123, v124, v125, v126, v127, v128, v129, v132, 1, v141, v130, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 98, 99, 4, 8, 2, 100) -> f_354(v123, v124, v125, v126, v127, v128, v129, v132, 1, v141, v130, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 98, 99, 4, 8, 2, 100) :|: 0 = 0 20.02/6.96 f_354(v123, v124, v125, v126, v127, v128, v129, v132, 1, v141, v130, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 98, 99, 4, 8, 2, 100) -> f_356(v123, v124, v125, v126, v127, v128, v129, v132, 1, v141, v130, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 98, 99, 4, 8, 2, 100) :|: TRUE 20.02/6.96 f_356(v123, v124, v125, v126, v127, v128, v129, v132, 1, v141, v130, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 98, 99, 4, 8, 2, 100) -> f_358(v123, v124, v125, v126, v127, v128, v129, v132, 1, v141, v130, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 98, 99, 4, 8, 2, 100) :|: TRUE 20.02/6.96 f_358(v123, v124, v125, v126, v127, v128, v129, v132, 1, v141, v130, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 98, 99, 4, 8, 2, 100) -> f_360(v123, v124, v125, v126, v127, v128, v129, v132, 1, v141, v130, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 98, 99, 4, 8, 2, 100) :|: 0 = 0 20.02/6.96 f_360(v123, v124, v125, v126, v127, v128, v129, v132, 1, v141, v130, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 98, 99, 4, 8, 2, 100) -> f_362(v123, v124, v125, v126, v127, v128, v129, v132, 1, v141, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 99, 4, 8, 2, 100) :|: 0 = 0 20.02/6.96 f_362(v123, v124, v125, v126, v127, v128, v129, v132, 1, v141, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 99, 4, 8, 2, 100) -> f_364(v123, v124, v125, v126, v127, v128, v129, v132, 1, v141, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 99, 4, 8, 2, 100) :|: v141 = 1 + v132 20.02/6.96 f_364(v123, v124, v125, v126, v127, v128, v129, v132, 1, v141, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 99, 4, 8, 2, 100) -> f_366(v123, v124, v125, v126, v127, v128, v129, v132, 1, v141, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 99, 4, 8, 2, 100) :|: TRUE 20.02/6.96 f_366(v123, v124, v125, v126, v127, v128, v129, v132, 1, v141, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 99, 4, 8, 2, 100) -> f_368(v123, v124, v125, v126, v127, v128, v129, v132, 1, v141, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 99, 4, 8, 2, 100) :|: TRUE 20.02/6.96 f_368(v123, v124, v125, v126, v127, v128, v129, v132, 1, v141, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 99, 4, 8, 2, 100) -> f_339(v123, v124, v125, v126, v127, v128, v129, v132, 1, v141, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 99, 100, 4, 8) :|: TRUE 20.02/6.96 f_339(v123, v124, v125, v126, v127, v128, v129, v130, 1, v132, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 99, 100, 4, 8) -> f_340(v123, v124, v125, v126, v127, v128, v129, v130, 1, v132, v133, v134, v135, v136, v137, v138, v139, 0, 3, 7, 99, 100, 4, 8) :|: 0 = 0 20.02/6.96 Combined rules. Obtained 1 rulesP rules: 20.02/6.96 f_340(v123:0, v124:0, v125:0, v126:0, v127:0, v128:0, v129:0, v130:0, 1, v132:0, v133:0, v134:0, v135:0, v136:0, v137:0, v138:0, v139:0, 0, 3, 7, 99, 100, 4, 8) -> f_340(v123:0, v124:0, v125:0, v126:0, v127:0, v128:0, v129:0, v132:0, 1, 1 + v132:0, v133:0, v134:0, v135:0, v136:0, v137:0, v138:0, v139:0, 0, 3, 7, 99, 100, 4, 8) :|: v130:0 < 99 && v132:0 < 100 && v132:0 > 0 20.02/6.96 Filtered unneeded arguments: 20.02/6.96 f_340(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24) -> f_340(x8, x10) 20.02/6.96 Removed division, modulo operations, cleaned up constraints. Obtained 1 rules.P rules: 20.02/6.96 f_340(v130:0, v132:0) -> f_340(v132:0, 1 + v132:0) :|: v132:0 < 100 && v132:0 > 0 && v130:0 < 99 20.02/6.96 20.02/6.96 ---------------------------------------- 20.02/6.96 20.02/6.96 (16) 20.02/6.96 Obligation: 20.02/6.96 Rules: 20.02/6.96 f_340(v130:0, v132:0) -> f_340(v132:0, 1 + v132:0) :|: v132:0 < 100 && v132:0 > 0 && v130:0 < 99 20.02/6.96 20.02/6.96 ---------------------------------------- 20.02/6.96 20.02/6.96 (17) IntTRSCompressionProof (EQUIVALENT) 20.02/6.96 Compressed rules. 20.02/6.96 ---------------------------------------- 20.02/6.96 20.02/6.96 (18) 20.02/6.96 Obligation: 20.02/6.96 Rules: 20.02/6.96 f_340(v130:0:0, v132:0:0) -> f_340(v132:0:0, 1 + v132:0:0) :|: v132:0:0 < 100 && v132:0:0 > 0 && v130:0:0 < 99 20.02/6.96 20.02/6.96 ---------------------------------------- 20.02/6.96 20.02/6.96 (19) RankingReductionPairProof (EQUIVALENT) 20.02/6.96 Interpretation: 20.02/6.96 [ f_340 ] = -1*f_340_2 20.02/6.96 20.02/6.96 The following rules are decreasing: 20.02/6.96 f_340(v130:0:0, v132:0:0) -> f_340(v132:0:0, 1 + v132:0:0) :|: v132:0:0 < 100 && v132:0:0 > 0 && v130:0:0 < 99 20.02/6.96 20.02/6.96 The following rules are bounded: 20.02/6.96 f_340(v130:0:0, v132:0:0) -> f_340(v132:0:0, 1 + v132:0:0) :|: v132:0:0 < 100 && v132:0:0 > 0 && v130:0:0 < 99 20.02/6.96 20.02/6.96 20.02/6.96 ---------------------------------------- 20.02/6.96 20.02/6.96 (20) 20.02/6.96 YES 20.61/6.99 EOF